stellar streams

using stellar streams to learn about the Milky Way's potential and dark matter subhalos

The halo of the Galaxy is rich in substructure. This substructure is the result of The Milky Way accreting material from smaller satellite galaxies. Debris from the satellites is tidally stripped by the Milky Way, forming long tidal streams of stars. These structures are of interest as they reveal something about the gravitational potential of the Galaxy, and hence the underlying dark matter distribution.

An N-body simulation of a stellar stream

I have done some work investigating the best way to find the potential using tidal stream data. The structure of a tidal stream is particularly simple when viewed in angle-action coordinates (see below). These special coordinates are linked to the shape of the gravitational potential of the Galaxy, so the stream will look correct in these coordinates only when we pick the correct gravitational potential.

As streams are so narrow, they provide sensitive probes of the presence of substructure in the Galactic halo. When a dark subhalo passes near a stream, it punches a hole through it producing a visible gap. Our models can incorporate these effects and indeed it appears that the Palomar 5 stream has a level of substructure consistent with that predicted by simulations.

(Sanders et al. 2016; Sanders 2014; Sanders & Binney 2013; Sanders & Binney 2013; Bovy et al. 2017; Erkal et al. 2016; Erkal et al. 2016; Brooks et al. 2025; Brooks et al. 2024)

References

2025

ApJ
LMC Calls, Milky Way Halo Answers: Disentangling the Effects of the MW–LMC Interaction on Stellar Stream Populations

Richard A. N. Brooks, Nicolás Garavito-Camargo, Kathryn V. Johnston, and 3 more authors

ApJ, Jan 2025

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The infall of the LMC into the Milky Way (MW) has dynamical implications throughout the MW’s dark matter halo. We study the impact of this merger on the statistical properties of populations of simulated stellar streams. Specifically, we investigate the radial and on-sky angular dependence of stream perturbations caused by the direct effect of stream–LMC interactions and/or the response of the MW dark matter halo. We use a time-evolving MW–LMC simulation described by basis function expansions to simulate streams. We quantify the degree of perturbation using a set of stream property statistics including the misalignment of proper motions with the stream track. In the outer halo, direct stream–LMC interactions produce a statistically significant effect, boosting the fraction of misaligned proper motions by \(∼\) 25% relative to the model with no LMC. Moreover, there is on-sky angular dependence of stream perturbations: the highest fractions of perturbed streams coincide with the same on-sky quadrant as the present-day LMC location. In the inner halo, the MW halo dipole response primarily drives stream perturbations, but it remains uncertain whether this is a detectable signature distinct from the LMC’s influence. For the fiducial MW–LMC model, we find agreement between the predicted fraction of streams with significantly misaligned proper motions, , and Dark Energy Survey data. Finally, we predict this fraction for the Rubin Observatory Legacy Survey of Space and Time (LSST) footprint. Using LSST data will improve our constraints on dark matter models and LMC properties, as it is sensitive to both.
@article{2025ApJ...978...79B, author = {{Brooks}, Richard A.~N. and {Garavito-Camargo}, Nicol{\'a}s and {Johnston}, Kathryn V. and {Price-Whelan}, Adrian M. and {Sanders}, Jason L. and {Lilleengen}, Sophia}, title = {{LMC Calls, Milky Way Halo Answers: Disentangling the Effects of the MW{\textendash}LMC Interaction on Stellar Stream Populations}}, journal = {\apj}, keywords = {Milky Way dynamics, Large Magellanic Cloud, Stellar streams, 1051, 903, 2166, Astrophysics - Astrophysics of Galaxies, Astrophysics - Cosmology and Nongalactic Astrophysics}, year = {2025}, month = jan, volume = {978}, number = {1}, eid = {79}, pages = {79}, doi = {10.3847/1538-4357/ad93a7}, archiveprefix = {arXiv}, eprint = {2410.02574}, primaryclass = {astro-ph.GA}, adsurl = {https://ui.adsabs.harvard.edu/abs/2025ApJ...978...79B}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} }

2024

MNRAS
Action and energy clustering of stellar streams in deforming Milky Way dark matter haloes

Richard A. N. Brooks, Jason L. Sanders, Sophia Lilleengen, and 2 more authors

MNRAS, Aug 2024

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We investigate the non-adiabatic effect of time-dependent deformations in the Milky Way (MW) halo potential on stellar streams. Specifically, we consider the MW’s response to the infall of the Large Magellanic Cloud (LMC) and how this impacts our ability to recover the spherically averaged MW mass profile from observation using stream actions. Previously, action clustering methods have only been applied to static or adiabatic MW systems to constrain the properties of the host system. We use a time- evolving MW-LMC simulation described by basis function expansions. We find that for streams with realistic observational uncertainties on shorter orbital periods and without close encounters with the LMC, e.g. GD-1, the radial action distribution is sufficiently clustered to locally recover the spherical MW mass profile across the stream radial range within a \(2σ\) confidence interval determined using a Fisher information approach. For streams with longer orbital periods and close encounters with the LMC, e.g. Orphan-Chenab (OC), the radial action distribution disperses as the MW halo has deformed non-adiabatically. Hence, for OC streams generated in potentials that include an MW halo with any deformations, action clustering methods will fail to recover the spherical mass profile within a \(2σ\) uncertainty. Finally, we investigate whether the clustering of stream energies can provide similar constraints. Surprisingly, we find for OC-like streams, the recovered spherically averaged mass profiles demonstrate less sensitivity to the time-dependent deformations in the potential.
@article{2024MNRAS.532.2657B, author = {{Brooks}, Richard A.~N. and {Sanders}, Jason L. and {Lilleengen}, Sophia and {Petersen}, Michael S. and {Pontzen}, Andrew}, title = {{Action and energy clustering of stellar streams in deforming Milky Way dark matter haloes}}, journal = {\mnras}, keywords = {Astrophysics - Astrophysics of Galaxies, Astrophysics - Cosmology and Nongalactic Astrophysics}, year = {2024}, month = aug, volume = {532}, number = {2}, pages = {2657-2673}, doi = {10.1093/mnras/stae1565}, archiveprefix = {arXiv}, eprint = {2401.11990}, primaryclass = {astro-ph.GA}, adsurl = {https://ui.adsabs.harvard.edu/abs/2024MNRAS.532.2657B}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} }

2017

MNRAS
Linear perturbation theory for tidal streams and the small-scale CDM power spectrum

Jo Bovy, Denis Erkal, and Jason L. Sanders

MNRAS, Apr 2017

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Tidal streams in the Milky Way are sensitive probes of the population of low-mass dark matter subhaloes predicted in cold dark matter (CDM) simulations. We present a new calculus for computing the effect of subhalo fly-bys on cold streams based on the action- angle representation of streams. The heart of this calculus is a line-of-parallel-angle approach that calculates the perturbed distribution function of a stream segment by undoing the effect of all relevant impacts. This approach allows one to compute the perturbed stream density and track in any coordinate system in minutes for realizations of the subhalo distribution down to 10\(^5\) M\(_\(⊙\) \) , accounting for the stream’s internal dispersion and overlapping impacts. We study the statistical properties of density and track fluctuations with large suites of simulations of the effect of subhalo fly- bys. The one-dimensional density and track power spectra along the stream trace the subhalo mass function, with higher mass subhaloes producing power only on large scales, while lower mass subhaloes cause structure on smaller scales. We also find significant density and track bispectra that are observationally accessible. We further demonstrate that different projections of the track all reflect the same pattern of perturbations, facilitating their observational measurement. We apply this formalism to data for the Pal 5 stream and make a first rigorous determination of 10\^{+11}_{-6} dark matter subhaloes with masses between 10\(^6.5\) and 10\(^9\) M\(_\(⊙\) \) within 20 kpc from the Galactic centre [corresponding to 1.4\^{+1.6}_{-0.9} times the number predicted by CDM-only simulations or to f\(_sub\) (r < 20 kpc) \(≈\) 0.2 per cent] assuming that the Pal 5 stream is 5 Gyr old. Improved data will allow measurements of the subhalo mass function down to 10\(^5\) M\(_\(⊙\) \) , thus definitively testing whether dark matter is clumpy on the smallest scales relevant for galaxy formation.
@article{2017MNRAS.466..628B, author = {{Bovy}, Jo and {Erkal}, Denis and {Sanders}, Jason L.}, title = {{Linear perturbation theory for tidal streams and the small-scale CDM power spectrum}}, journal = {\mnras}, keywords = {Galaxy: fundamental parameters, Galaxy: halo, Galaxy: kinematics and dynamics, Galaxy: structure, dark matter, Astrophysics - Astrophysics of Galaxies, Astrophysics - Cosmology and Nongalactic Astrophysics}, year = {2017}, month = apr, volume = {466}, number = {1}, pages = {628-668}, doi = {10.1093/mnras/stw3067}, archiveprefix = {arXiv}, eprint = {1606.03470}, primaryclass = {astro-ph.GA}, adsurl = {https://ui.adsabs.harvard.edu/abs/2017MNRAS.466..628B}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} }

2016

MNRAS
Dynamics of stream-subhalo interactions

Jason L. Sanders, Jo Bovy, and Denis Erkal

MNRAS, Apr 2016

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We develop a formalism for modelling the impact of dark matter subhaloes on cold thin streams. Our formalism models the formation of a gap in a stream in angle-frequency space and is able to handle general stream and impact geometry. We analyse an N-body simulation of a cold stream formed from a progenitor on an eccentric orbit in an axisymmetric potential, which is perturbed by a direct impact from a 10\(^8\) M\(_\(⊙\) \) subhalo, and produce a complete generative model of the perturbed stream that matches the simulation well at a range of times. We show how the results in angle-frequency space can be related to physical properties of the gaps and that previous results for more constrained simulations are recovered. We demonstrate how our results are dependent upon the mass of the subhalo and the location of the impact along the stream. We find that gaps formed far downstream grow more rapidly than those closer to the progenitor due to the more ordered nature of the stream members far from the progenitor. Additionally, we show that the minimum gap density plateaus in time at a value that decreases with increasing subhalo mass.
@article{2016MNRAS.457.3817S, author = {{Sanders}, Jason L. and {Bovy}, Jo and {Erkal}, Denis}, title = {{Dynamics of stream-subhalo interactions}}, journal = {\mnras}, keywords = {Galaxy: halo, Galaxy: kinematics and dynamics, Galaxy: structure, cosmology: theory, dark matter, Astrophysics - Astrophysics of Galaxies}, year = {2016}, month = apr, volume = {457}, number = {4}, pages = {3817-3835}, doi = {10.1093/mnras/stw232}, archiveprefix = {arXiv}, eprint = {1510.03426}, primaryclass = {astro-ph.GA}, adsurl = {https://ui.adsabs.harvard.edu/abs/2016MNRAS.457.3817S}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} }
MNRAS
The number and size of subhalo-induced gaps in stellar streams

Denis Erkal, Vasily Belokurov, Jo Bovy, and 1 more author

MNRAS, Nov 2016

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Ample observational capabilities exist today to detect the small density perturbations that low-mass dark matter subhaloes impart on stellar streams from disrupting Galactic satellites. In anticipation of these observations, we investigate the expected number and size of gaps by combining an analytic prescription for gap evolution on circular orbits with the flux of subhaloes near the stream. We explore the distribution of gap sizes and depths for a typical cold stream around the Milky Way and find that for a given stream age and gap depth, each subhalo mass produces a characteristic gap size. For a stream with an age of a few Gyr, orbiting at a distance of 10-20 kpc from the Galactic centre, even modest subhaloes with a mass of 10\(^6\) -10\(^7\) M\(_\(⊙\) \) produce gaps with sizes that are of the order of several degrees. We consider the number and distribution of gap sizes created by subhaloes with masses 10\(^5\) -10\(^9\) M\(_\(⊙\) \) , accounting for the expected depletion of subhaloes by the Milky Way disc, and present predictions for six cold streams around the Milky Way. For Pal 5, we forecast 0.7 gaps with a density depletion of at least 25 per cent and a typical gap size of 8\textdegree. Thus, there appears to be no tension between the recent non-detection of density depletions in the Pal 5 tidal tails and \(Λ\) CDM expectations. These predictions can be used to guide the scale of future gap searches.
@article{2016MNRAS.463..102E, author = {{Erkal}, Denis and {Belokurov}, Vasily and {Bovy}, Jo and {Sanders}, Jason L.}, title = {{The number and size of subhalo-induced gaps in stellar streams}}, journal = {\mnras}, keywords = {Galaxy: fundamental parameters, galaxies: haloes, galaxies: structure, dark matter, Astrophysics - Astrophysics of Galaxies}, year = {2016}, month = nov, volume = {463}, number = {1}, pages = {102-119}, doi = {10.1093/mnras/stw1957}, archiveprefix = {arXiv}, eprint = {1606.04946}, primaryclass = {astro-ph.GA}, adsurl = {https://ui.adsabs.harvard.edu/abs/2016MNRAS.463..102E}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} }
MNRAS
Stray, swing and scatter: angular momentum evolution of orbits and streams in aspherical potentials

Denis Erkal, Jason L. Sanders, and Vasily Belokurov

MNRAS, Sep 2016

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In aspherical potentials orbital planes continuously evolve. The gravitational torques impel the angular momentum vector to precess, that is to slowly stray around the symmetry axis, and nutate, I.e. swing up and down periodically in the perpendicular direction. This familiar orbital pole motion - if detected and measured - can reveal the shape of the underlying gravitational potential, the quantity only crudely gauged in the Galaxy so far. Here we demonstrate that the debris poles of stellar tidal streams show a very similar straying and swinging behaviour, and give analytic expressions to link the amplitude and the frequency of the pole evolution to the flattening of the dark matter distribution. While these results are derived for near- circular orbits, we show they are also valid for eccentric orbits. Most importantly, we explain how the differential orbital plane precession leads to the broadening of the stream and show that streams on polar orbits ought to scatter faster. We provide expressions for the stream width evolution as a function of the axisymmetric potential flattening and the angle from the symmetry plane and prove that our models are in good agreement with streams produced in N-body simulations. Interestingly, the same intuition applies to streams whose progenitors are on short- or long-axis loops in a triaxial potential. Finally, we present a compilation of the Galactic cold stream data, and discuss how the simple picture developed here, along with stream modelling, can be used to constrain the symmetry axes and flattening of the Milky Way.
@article{2016MNRAS.461.1590E, author = {{Erkal}, Denis and {Sanders}, Jason L. and {Belokurov}, Vasily}, title = {{Stray, swing and scatter: angular momentum evolution of orbits and streams in aspherical potentials}}, journal = {\mnras}, keywords = {galaxies: haloes, galaxies: structure, dark matter, Astrophysics - Astrophysics of Galaxies}, year = {2016}, month = sep, volume = {461}, number = {2}, pages = {1590-1604}, doi = {10.1093/mnras/stw1400}, archiveprefix = {arXiv}, eprint = {1603.08922}, primaryclass = {astro-ph.GA}, adsurl = {https://ui.adsabs.harvard.edu/abs/2016MNRAS.461.1590E}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} }

2014

MNRAS

Probabilistic model for constraining the Galactic potential using tidal streams

Jason L. Sanders

MNRAS, Sep 2014

Abs ADS arXiv pdf Bib DOI

We present a generative probabilistic model for a tidal stream and demonstrate how this model is used to constrain the Galactic potential. The model takes advantage of the simple structure of a stream in angle and frequency space for the correct potential. We investigate how the method performs on full 6D mock stream data, and mock data with outliers included. As currently formulated, the technique is computationally costly when applied to data with large observational errors, but we describe several modifications that promise to make the technique computationally tractable.

@article{2014MNRAS.443..423S,
  author = {{Sanders}, Jason L.},
  title = {{Probabilistic model for constraining the Galactic potential using tidal streams}},
  journal = {\mnras},
  keywords = {methods: numerical, Galaxy: kinematics and dynamics, Galaxy: structure, galaxies: kinematics and dynamics, Astrophysics - Astrophysics of Galaxies},
  year = {2014},
  month = sep,
  volume = {443},
  number = {1},
  pages = {423-431},
  doi = {10.1093/mnras/stu1159},
  archiveprefix = {arXiv},
  eprint = {1401.7602},
  primaryclass = {astro-ph.GA},
  adsurl = {https://ui.adsabs.harvard.edu/abs/2014MNRAS.443..423S},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

2013

MNRAS
Stream-orbit misalignment - II. A new algorithm to constrain the Galactic potential

Jason L. Sanders, and James Binney

MNRAS, Aug 2013

Abs ADS arXiv pdf Bib DOI

In the first of these two papers, we demonstrated that assuming streams delineate orbits can lead to order one errors in potential parameters for realistic Galactic potentials. Motivated by the need for an improvement on orbit-fitting, we now present an algorithm for constraining the Galactic potential using tidal streams without assuming that streams delineate orbits. This approach is independent of the progenitor mass so is valid for all observed tidal streams. The method makes heavy use of angle- action variables and seeks the potential which recovers the expected correlations in angle space. We demonstrate that the method can correctly recover the parameters of a simple two- parameter logarithmic potential by analysing an N-body simulation of a stream. We investigate the magnitude of the errors in observational data for which the method can still recover the correct potential and compare this to current and future errors in data. The errors in the observables of individual stars for current and near future data are shown to be too large for the direct use of this method, but when the data are averaged in bins on the sky, the resulting averaged data are accurate enough to constrain correctly the potential parameters for achievable observational errors. From pseudo-data with errors comparable to those that will be furnished in the era of Gaia (20 per cent distance errors, 1.2 mas yr\(^-1\) proper motion errors, and 10 km s\(^-1\) line-of-sight velocity errors) we recover the circular velocity, V\(_c\) = 220 km s\(^- 1\) , and the flattening of the potential, q = 0.9, to be V\(_c\) = 223 \(\pm\) 10 km s\(^- 1\) and q = 0.91 \(\pm\) 0.09.
@article{2013MNRAS.433.1826S, author = {{Sanders}, Jason L. and {Binney}, James}, title = {{Stream-orbit misalignment - II. A new algorithm to constrain the Galactic potential}}, journal = {\mnras}, keywords = {methods: numerical, Galaxy: halo, Galaxy: kinematics and dynamics, Galaxy: structure, galaxies: kinematics and dynamics, Astrophysics - Astrophysics of Galaxies}, year = {2013}, month = aug, volume = {433}, number = {3}, pages = {1826-1836}, doi = {10.1093/mnras/stt816}, archiveprefix = {arXiv}, eprint = {1305.1937}, primaryclass = {astro-ph.GA}, adsurl = {https://ui.adsabs.harvard.edu/abs/2013MNRAS.433.1826S}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} }
MNRAS
Stream-orbit misalignment - I. The dangers of orbit-fitting

Jason L. Sanders, and James Binney

MNRAS, Aug 2013

Abs ADS arXiv pdf Bib DOI

Tidal streams do not, in general, delineate orbits. A stream-orbit misalignment is expected to lead to biases when using orbit- fitting to constrain models for the Galactic potential. In this first of two papers, we discuss the expected magnitude of the misalignment and the resulting dangers of using orbit-fitting algorithms to constrain the potential. We summarize data for known streams which should prove useful for constraining the Galactic potential, and compute their actions in a realistic Galactic potential. We go on to discuss the formation of tidal streams in angle-action space, and explain why, in general, streams do not delineate orbits. The magnitude of the stream- orbit misalignment is quantified for a logarithmic potential and a multicomponent Galactic potential. Specifically, we focus on the expected misalignment for the known streams. By introducing a two-parameter family of realistic Galactic potentials we demonstrate that assuming that these streams delineate orbits can lead to order one errors in the halo flattening and halo-to- disc force ratio at the Sun. We present a discussion of the dependence of these results on the progenitor mass and demonstrate that the misalignment is mass independent for the range of masses of observed streams. Hence, orbit-fitting does not yield better constraints on the potential if one uses narrower, lower mass streams.
@article{2013MNRAS.433.1813S, author = {{Sanders}, Jason L. and {Binney}, James}, title = {{Stream-orbit misalignment - I. The dangers of orbit-fitting}}, journal = {\mnras}, keywords = {Galaxy: halo, Galaxy: kinematics and dynamics, Galaxy: structure, galaxies: kinematics and dynamics, Astrophysics - Astrophysics of Galaxies}, year = {2013}, month = aug, volume = {433}, number = {3}, pages = {1813-1825}, doi = {10.1093/mnras/stt806}, archiveprefix = {arXiv}, eprint = {1305.1935}, primaryclass = {astro-ph.GA}, adsurl = {https://ui.adsabs.harvard.edu/abs/2013MNRAS.433.1813S}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} }